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Tentukan nilai limit fungsi berikut. 5. t → − 2 lim ​ t + 2 2 t 2 + 12 t + 16 ​

Tentukan nilai limit fungsi berikut.

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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nilai dari .

nilai dari begin mathsize 14px style limit as t rightwards arrow negative 2 of space fraction numerator 2 t squared plus 12 t plus 16 over denominator t plus 2 end fraction equals 4 end style.

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Pembahasan

Diketahui: Pembagian limit fungsi. Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut: Substitusi dengan pada limit fungsi yang telah disederhanakan seperti berikut: Jadi, nilai dari .

Diketahui:

Pembagian limit fungsi.

Sederhanakan limit fungsi yang diketahui menggunakan metode pemfaktoran seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as t rightwards arrow negative 2 of space fraction numerator 2 t squared plus 12 t plus 16 over denominator t plus 2 end fraction end cell equals cell limit as t rightwards arrow negative 2 of space fraction numerator 2 open parentheses t squared plus 6 t plus 8 close parentheses over denominator t plus 2 end fraction end cell row blank equals cell limit as t rightwards arrow negative 2 of space fraction numerator 2 open parentheses t squared plus 4 t plus 2 t plus 8 close parentheses over denominator t plus 2 end fraction end cell row blank equals cell limit as t rightwards arrow negative 2 of space fraction numerator 2 open parentheses t open parentheses t plus 4 close parentheses plus 2 open parentheses t plus 4 close parentheses close parentheses over denominator t plus 2 end fraction end cell row blank equals cell limit as t rightwards arrow negative 2 of space fraction numerator 2 down diagonal strike open parentheses t plus 2 close parentheses end strike open parentheses t plus 4 close parentheses over denominator down diagonal strike t plus 2 end strike end fraction end cell row blank equals cell limit as t rightwards arrow negative 2 of space 2 open parentheses t plus 4 close parentheses end cell row blank equals cell limit as t rightwards arrow negative 2 of space 2 t plus 8 end cell end table end style

Substitusi begin mathsize 14px style t end style dengan begin mathsize 14px style negative 2 end style pada limit fungsi yang telah disederhanakan seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as t rightwards arrow negative 2 of space 2 t plus 8 end cell equals cell 2 open parentheses negative 2 close parentheses plus 8 end cell row blank equals cell negative 4 plus 8 end cell row blank equals 4 end table end style

Jadi, nilai dari begin mathsize 14px style limit as t rightwards arrow negative 2 of space fraction numerator 2 t squared plus 12 t plus 16 over denominator t plus 2 end fraction equals 4 end style.

48

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